Statistical Theory of Effective Viscosity in a Random Suspension

Abstract

A general theory is presented to derive the coarse-grained equations governing the macroscopic behaviour of slow viscous flow in suspensions from the standpoint of statistical continuum mechanics. A system of equations governing the macroscopic behaviour of viscous flow in suspensions can be obtained using formal perturbation methods and coarse-graining procedures. The coarse-grained equations lead to an expression for the dependence of the effective viscosity of suspensions on the concentration of particles φ. In the dilute limit our result reduces to Einstein’s theory of dilute suspensions, and the deviation from Batchelor’s formula is not significant to the second order in φ. Even for more concentrated suspensions, the result is in good agreement with experimental data obtained by Vand.